matlab - SVD speed in CPU and GPU

Question

I'm testing svd in Matlab R2014a and it seems that there is no CPU vs GPU speedup. I'm using a GTX 460 card and a Core 2 duo E8500.

Here is my code:

%test SVD
n=10000;
%host
Mh= rand(n,1000);
tic
%[Uh,Sh,Vh]= svd(Mh);
svd(Mh);
toc
%device
Md = gpuArray.rand(n,1000);
tic
%[Ud,Sd,Vd]= svd(Md);
svd(Md);
toc

Also, the run times are different from run to run, but the CPU and GPU versions are about the same. Why there is no speedup?

Here are some tests

for i=1:10
    clear;
    m= 10000;
    n= 100;
    %host
    Mh= rand(m,n);
    tic
    [Uh,Sh,Vh]= svd(Mh);
    toc
    %device
    Md = gpuArray.rand(m,n);
    tic
    [Ud,Sd,Vd]= svd(Md);
    toc
end

>> test_gpu_svd
Elapsed time is 43.124130 seconds.
Elapsed time is 43.842277 seconds.
Elapsed time is 42.993283 seconds.
Elapsed time is 44.293410 seconds.
Elapsed time is 42.924541 seconds.
Elapsed time is 43.730343 seconds.
Elapsed time is 43.125938 seconds.
Elapsed time is 43.645095 seconds.
Elapsed time is 43.492129 seconds.
Elapsed time is 43.459277 seconds.
Elapsed time is 43.327012 seconds.
Elapsed time is 44.040959 seconds.
Elapsed time is 43.242291 seconds.
Elapsed time is 43.390881 seconds.
Elapsed time is 43.275379 seconds.
Elapsed time is 43.408705 seconds.
Elapsed time is 43.320387 seconds.
Elapsed time is 44.232156 seconds.
Elapsed time is 42.984002 seconds.
Elapsed time is 43.702430 seconds.


for i=1:10
    clear;
    m= 10000;
    n= 100;
    %host
    Mh= rand(m,n,'single');
    tic
    [Uh,Sh,Vh]= svd(Mh);
    toc
    %device
    Md = gpuArray.rand(m,n,'single');
    tic
    [Ud,Sd,Vd]= svd(Md);
    toc
end

>> test_gpu_svd
Elapsed time is 21.140301 seconds.
Elapsed time is 21.334361 seconds.
Elapsed time is 21.275991 seconds.
Elapsed time is 21.582602 seconds.
Elapsed time is 21.093408 seconds.
Elapsed time is 21.305413 seconds.
Elapsed time is 21.482931 seconds.
Elapsed time is 21.327842 seconds.
Elapsed time is 21.120969 seconds.
Elapsed time is 21.701752 seconds.
Elapsed time is 21.117268 seconds.
Elapsed time is 21.384318 seconds.
Elapsed time is 21.359225 seconds.
Elapsed time is 21.911570 seconds.
Elapsed time is 21.086259 seconds.
Elapsed time is 21.263040 seconds.
Elapsed time is 21.472175 seconds.
Elapsed time is 21.561370 seconds.
Elapsed time is 21.330314 seconds.
Elapsed time is 21.546260 seconds.

Answer 1

Generally SVD is a difficult to paralellize routine. You can check here that with a high end Tesla card, the speedup is not very impressive.

You have a GTX460 card - Fermi architecture. The card is optimized for gaming (single precision computations), not HPC (double precision computation). The Single Precision / Double Precision throughput ratio is 12. So the card has 873 GFLOPS SP / 72 GFLOPS DP. Check here.

So if the Md array uses double precision elements, then the computation on it would be rather slow. Also there's a high chance that when calling the CPU routine, all CPU cores will get utilized, reducing the possible gain of running the routine on the GPU. Plus, in the GPU run you pay time for transferring the buffer to the device.

Per Divakar's suggestion, you could use Md = single(Md) to convert your array to single precision and run the benchmark again. You can try and go with a bigger dataset size to see if something changes. I don't expect to much gain for this routine on your GPU.

Update 1:

After you posted the results, I saw that the DP/SP time ratio is 2. On the CPU side this is normal, because you can fit 2 times less double values in SSE registers. However, a ratio of only 2 on the GPU side means that the gpu code does not make best use of the SM cores - because the theoretical ratio is 12. In other words, I would have expected much better SP performance for an optimized code, compared to DP. It seems that this is not the case.